Details

analyze3.4s (14.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2392	341
1	2392	341
0	5	5
1	5	5

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
1.2%	98.6%	0.2%	12
1.8%	98%	0.2%	13
2%	97.7%	0.2%	14

Symmetry

sort(lambda1 lambda2)

sort(phi1 phi2)

Compiler

Compiled 20 to 18 computations (10% saved)

sample232.0ms (1%)

Algorithm

1×

intervals

Results

155.0ms	180×	body	1024	valid
27.0ms	40×	body	512	valid
10.0ms	6×	body	2048	valid
7.0ms	20×	body	256	valid
2.0ms	10×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	96	31
1	96	31

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

14.8b

Counts

2 → 1

Compiler

Compiled 38 to 34 computations (10.5% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
1.2b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
3.0b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite96.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

3.3b

Rules

13×	`add-sqr-sqrt_binary64_1464`
9×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
8×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
6×	`associate-l_binary64_1383` `associate-r_binary64_1382`
4×	`cos-sum_binary64_1576` `add-log-exp_binary64_1481`
3×	`cancel-sign-sub-inv_binary64_1408`
2×	`pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `*-commutative_binary64_1373`
1×	`cos-diff_binary64_1579` `sub-neg_binary64_1435` `acos-asin_binary64_1623` `sin-mult_binary64_1597`

Counts

4 → 57

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
3.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 1667 to 309 computations (81.5% saved)

series506.0ms (2.1%)

Error

14.2b

Counts

4 → 45

Calls

4 calls:

247.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
94.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
75.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
53.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 2600 to 1581 computations (39.2% saved)

simplify98.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5231	2258

prune132.0ms (0.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	88	14	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	14	103

Error

3.3b

Counts

103 → 14

Compiler

Compiled 2815 to 610 computations (78.3% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
1.2b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite96.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

3.2b

Rules

16×	`add-sqr-sqrt_binary64_1464`
10×	`pow1_binary64_1503` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
9×	`associate-l_binary64_1383` `associate-r_binary64_1382`
4×	`add-log-exp_binary64_1481`
3×	`pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `*-commutative_binary64_1373`
2×	`sin-mult_binary64_1597`
1×	`acos-asin_binary64_1623`

Counts

4 → 64

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
3.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

Compiler

Compiled 2362 to 361 computations (84.7% saved)

series754.0ms (3.1%)

Error

3.3b

Counts

4 → 44

Calls

4 calls:

370.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
150.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
100.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
90.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 3930 to 2051 computations (47.8% saved)

simplify96.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4841	2974
1	4841	2974

prune140.0ms (0.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	98	10	108
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	107	15	122

Error

3.2b

Counts

122 → 15

Compiler

Compiled 3914 to 773 computations (80.3% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) R)
1.2b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
4.2b	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))

rewrite91.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

3.2b

Rules

13×	`add-sqr-sqrt_binary64_1464`
9×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
8×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
6×	`associate-l_binary64_1383` `associate-r_binary64_1382`
5×	`add-log-exp_binary64_1481`
3×	`log-pow_binary64_1531` `log-prod_binary64_1528`
2×	`pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `unswap-sqr_binary64_1410` `*-commutative_binary64_1373`
1×	`exp-to-pow_binary64_1504` `exp-prod_binary64_1494` `rem-log-exp_binary64_1483` `acos-asin_binary64_1623` `sin-mult_binary64_1597`

Counts

4 → 59

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
3.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) R)
2.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))

Compiler

Compiled 2357 to 308 computations (86.9% saved)

series988.0ms (4.1%)

Error

3.2b

Counts

4 → 44

Calls

4 calls:

375.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))) R)
310.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))
172.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (log.f64 (exp.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
90.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 4156 to 2196 computations (47.2% saved)

simplify81.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4929	2933
1	4929	2933

prune121.0ms (0.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	103	15	118

Error

3.2b

Counts

118 → 15

Compiler

Compiled 3806 to 714 computations (81.2% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(exp.f64 (log.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))
0.3b	(.f64 (exp.f64 (log.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
0.7b	(log.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
1.2b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))

rewrite99.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

3.2b

Rules

14×	`add-sqr-sqrt_binary64_1464`
10×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442` `log-prod_binary64_1528`
8×	`pow1_binary64_1503`
7×	`exp-sum_binary64_1488`
6×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `associate-l_binary64_1383`
4×	`add-log-exp_binary64_1481` `exp-prod_binary64_1494`
3×	`associate-r_binary64_1382`
2×	`log-pow_binary64_1531` `unswap-sqr_binary64_1410`
1×	`acos-asin_binary64_1623` `rem-log-exp_binary64_1483` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cbrt-unprod_binary64_1475` `*-commutative_binary64_1373` `rem-exp-log_binary64_1482`

Counts

4 → 57

Calls

4 calls:

6.0ms	(.f64 (exp.f64 (log.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
4.0ms	(exp.f64 (log.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))
1.0ms	(log.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))

Compiler

Compiled 2768 to 212 computations (92.3% saved)

series3.7s (15.3%)

Error

3.2b

Counts

4 → 51

Calls

4 calls:

1.5s	(.f64 (exp.f64 (log.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))) R)
1.1s	(exp.f64 (log.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))))
937.0ms	(log.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1))))))))
159.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))))))

Compiler

Compiled 5202 to 2576 computations (50.5% saved)

simplify112.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4859	4807
1	4859	4807

prune108.0ms (0.4%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	103	5	108
Fresh	1	12	13
Picked	1	0	1
Done	0	1	1
Total	105	18	123

Error

3.2b

Counts

123 → 18

Compiler

Compiled 3703 to 197 computations (94.7% saved)

regimes3.2s (13.2%)

Accuracy

Total 0.4b remaining (9.5%)

Threshold costs 0.4b (9.5%)

Compiler

Compiled 49123 to 29081 computations (40.8% saved)

bsearch0.0ms (0%)

simplify26.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	43
1	31	43

Removed

((sort phi1 phi2) (sort lambda1 lambda2))

Compiler

Compiled 104 to 88 computations (15.4% saved)

end0.0ms (0%)

sample10.1s (41.4%)

Algorithm

1×

intervals

Results

4.9s	5509×	body	1024	valid
792.0ms	1424×	body	512	valid
511.0ms	264×	body	2048	valid
182.0ms	508×	body	256	valid
51.0ms	295×	body	128	valid
0.0ms	1×	body	256	invalid

Compiler

Compiled 4441 to 2641 computations (40.5% saved)

Details

analyze3.4s (14.1%)

sample232.0ms (1%)

simplify10.0ms (0%)

prune3.0ms (0%)

localize19.0ms (0.1%)

rewrite96.0ms (0.4%)

series506.0ms (2.1%)

simplify98.0ms (0.4%)

prune132.0ms (0.5%)

localize26.0ms (0.1%)

rewrite96.0ms (0.4%)

series754.0ms (3.1%)

simplify96.0ms (0.4%)

prune140.0ms (0.6%)

localize28.0ms (0.1%)

rewrite91.0ms (0.4%)

series988.0ms (4.1%)

simplify81.0ms (0.3%)

prune121.0ms (0.5%)

localize30.0ms (0.1%)

rewrite99.0ms (0.4%)

series3.7s (15.3%)

simplify112.0ms (0.5%)

prune108.0ms (0.4%)

regimes3.2s (13.2%)

bsearch0.0ms (0%)

simplify26.0ms (0.1%)

end0.0ms (0%)

sample10.1s (41.4%)

Profiling